To find the equation of the line in slope-intercept form (y = mx + b) that passes through the points (-3, 6) and (9, 10), we first need to calculate the slope (m) using the slope formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points (-3, 6) and (9, 10):
- \(x_1 = -3\), \(y_1 = 6\)
- \(x_2 = 9\), \(y_2 = 10\)
Substituting these values into the slope formula:
\[ m = \frac{10 - 6}{9 - (-3)} = \frac{4}{9 + 3} = \frac{4}{12} = \frac{1}{3} \]
Now, we have the slope \(m = \frac{1}{3}\).
Next, we use one of the points to solve for the y-intercept (b) using the slope-intercept form equation \(y = mx + b\). We can use the point (-3, 6):
\[ 6 = \frac{1}{3}(-3) + b \]
Calculating this gives:
\[ 6 = -1 + b \] \[ b = 6 + 1 = 7 \]
Now we have both the slope and y-intercept. The equation of the line is:
\[ y = \frac{1}{3}x + 7 \]
Thus, the answer is:
B: \(y = \frac{1}{3}x + 7\)
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